Question 1194817
<pre>
To find the equation for f∘g(x), plug the entire right side of the 
equation for g(x), for x in the equation for f(x).

f(x) = 2x-1,   g(x) = 3x+1

So we plug (3x+1) in place of x in 2x-1 and get 2(3x+1)-1 which 
simplifies to 6x+2-1 or 6x+1, so the equation for f∘g(x) is

f∘g(x) = 6x+1.

Now we must find the domain for f∘g(x). 

Any value we substitute for x in f∘g(x) must:
(a) be in the domain of g(x).
(b) g(x) must produce a value in the domain of f(x)

g(x) has the domain  ]-1; 2[ 

So the domain for f∘g(x) must be contained entirely within this 
interval.

Since g(x) is linear, the endpoints of the range of g(x) is found
by substituting the end points of the domain of g(x) for x in the
equation for g(x): 3(-1)+2=-1, 3(2)+2=8 so g(x) produces the range
]-1; 8[ 

But f(x) has the domain  ]1; 10[ , so f(x) cannot be used for 
]-1; 1],
so we must remove  ]-1; 1]  from ]-1; 2[ which leaves ]1; 2[ 

So:

f∘g(x) = 6x+1, x ∈ ]1; 2[ 

Now you switch the roles of f and g and do part b) yourself.

Edwin</pre>